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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Orthogonal complement
Replies: 15   Last Post: Mar 5, 2013 6:48 PM

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Kaba

Posts: 289
Registered: 5/23/11
Orthogonal complement
Posted: Mar 3, 2013 10:43 AM
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Hi,

Let V be a finite-dimensional vector space over K together with a
reflexive bilinear form f : V^2 --> K, and let S subset V be a subspace
of V. Let C(S) stand for the orthogonal complement of S.

Claim
-----

The bilinear form f is non-degenerate if and only if V = S + C(S).

Any ideas?

--
http://kaba.hilvi.org

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